Asymptotics of the natural oscillations of a thin elastic gasket between absolutely rigid profiles

The asymptotics of the frequencies and modes of the natural oscillations of a thin elastic gasket between two absolutely rigid profiles are constructed. The localization and concentration of the stresses around the point of maximum thickness of the gasket are established and the character of its possible fracture is discussed. Spectral gaps, that is, stopping zones for waves, are observed in an infinite elastic periodic waveguide and the trapping of waves in the case of a local perturbation of its shape.